Photonic crystal

ABSTRACT

A photonic crystal comprises a plurality of elongated elements formed of a first dielectric material and arranged in a two-dimensional periodic honeycomb lattice. A second dielectric material surrounds the elongated elements and extending between them. The a second dielectric material defines between the elongated elements a plurality of spaces filled with a third dielectric material. The first dielectric material has permittivity that is greater than permittivity of the second dielectric material and permittivity of the third dielectric material.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to photonic crystals and methods forfabricating photonic crystals.

2. Description or the Related Art

Photonic crystals are of great interest in the field of photonicsbecause certain types of photonic crystals exhibit a photonic bandgap.The photonic bandgap defines a range of frequencies at whichelectromagnetic wave is not permitted to propagate it.

Different types of photonic crystals are proposed and tabulated on page862 in Baba, “Semiconductor Micro Resonators and Control of NaturalEmission”, Solid State Physics (Japanese), vol. 32, No. 11, 1997, pages859-869.

The typical photonic crystal is a spatially periodic structure. Onewell-known photonic crystal exhibits two-dimensional periodicity inwhich multiple elongated, e.g. cylindrical, elements made of adielectric material are in a two-dimensional periodic pattern with theirlongitudinal axes parallel to each other.

Joannopoulos et al., “Molding the Flow of Light” Photonic Crystals pages124-125, discuss the case of elongated elements in the form of aircolumns in dielectric along with a photonic bandgap map for a triangularlattice of air columns drilled in a dielectric medium havingpermittivity 11.4. FIG. 6 of the accompanying drawings illustrates thisphotonic bandgap map. It also considers “honeycomb lattice” along with aphotonic bandgap map for this structure. This photonic bandgap map ispresented in FIG. 7 of the accompanying drawings.

Referring to FIG. 6, the photonic bandgap map for triangular lattice ofair columns clearly indicates that for r/a around 0.45, the triangularlattice of air columns possesses a complete band gap for TB polarizationand TM polarization for frequencies around 0.45(2πc/a), where r is aradius of air column, a is a lattice constant, c is the speed of light.A complete band gap of the triangular lattice of air columns occurs at adiameter of d=0.95a, at a midgap frequency of ωa/2πc=0.48, where ω isangular frequency. Thus, this structure has very thin dielectric veinsof width 0.05a between the air columns. To fabricate such a structurewith a photonic bandgap at λ=1.5 μm would require a minimum feature sizeof 0.035 μm, where λ is a wavelength. Such fine feature size may befabricated, but this is very difficult.

Referring to FIG. 7, the photonic bandgap map for honeycomb lattice ofdielectric columns clearly shows a large overlap of photonic bandgapsfor TN and TE polarizations, around r/a=0.14 and ωa/2πc˜1, which is ofmuch larger extent than the complete band gap of the triangular lattice.To fabricate such a structure with a photonic bandgap at λ=1.5 μm wouldrequire a feature size of 0.45 μm. The production of suchtwo-dimensional honeycomb lattice is less difficult to fabricate,

An object of the present invention is to strengthen such a latticestructure having a complete band gap, i.e., an overlap of photonicbandgaps for TH and TN polarizations.

Another object of the present invention is to provide a method offabricating a structurally strengthened lattice, which is suited formass production.

SUMMARY OF THE INVENTION

According to one exemplary implementation of the invention, there isprovided a photonic crystal comprising:

a plurality of elongated elements formed of a first dielectric materialand arranged in a two-dimensional periodic honeycomb lattice; and

a second dielectric material surrounding said plurality of elongatedelements and extending between said plurality of first elements,

said second dielectric material defining between said elongated elementsa plurality of spaces filled with a third dielectric material,

said first dielectric material having permittivity that is greater thanpermittivity of said second dielectric material and permittivity of saidthird dielectric material.

According to another exemplary implementation of the invention, there isprovided a method of fabricating a photonic crystal, comprising:

providing a substrate;

forming within said substrate a plurality of elongated elements of afirst dielectric material in a two-dimensional periodic honeycomblattice;

forming a layer of a second dielectric material over said substrate to athickness such that said second dielectric material continuously extendbetween said plurality of elongated elements, said second dielectricmaterial having permittivity less than permittivity of said firstdielectric material.

According to other exemplary implementation of the invention, there isprovided a method of fabricating a photonic crystal, comprising:

providing a dielectric substrate,

oxidizing said substrate inwardly to define a plurality of elongatedelements within said substrate, and

controlling the depth of oxidation of said substrate to determinedimensions of each of said plurality of elongated elements.

According to a specific aspect of the invention, there is provided amethod of fabricating a photonic crystal, comprising;

providing a substrate;

forming elongated bores within said substrate in triangular lattice; and

oxidizing said substrate inwardly to define a plurality of elongatedelements within said substrate until a portion of said substrate on aline segment interconnecting centers of the adjacent two of said boresis completely oxidized.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features and advantages of theinvention will be apparent from the following more particulardescription of exemplary embodiments of the invention as illustrated inthe accompanying drawings in which like reference characters refer tothe same parts throughout the different views. The drawings are notnecessarily scale, emphasis instead being placed upon illustrating theprinciples of the invention.

FIG. 1 is a schematic top view of a first implementation of theinvention comprising a photonic crystal configured in two-dimensionalperiodic structure.

FIG. 2 is a schematic top view of a second implementation of theinvention comprising a photonic crystal configured in two-dimensionalperiodic structure.

FIGS. 3A-1 to 3C-1 are schematic cross-sectional illustrations showingfabrication steps used to produce a photonic crystal, illustrating athird implementation of the invention,

FIGS. 3A-2 to 3C-2 are schematic top views showing the fabrication stepsof FIGS. 3A-1 to 3C-1, respectively.

FIGS. 4A-1 to 4C-1 are schematic cross-sectional illustrations showingfabrication steps used to produce a photonic crystal, illustrating afourth implementation of the invention.

FIGS. 4A-2 to 4C-2 are schematic top views showing the fabrication stepsof FIGS. 4A-1 to 4C-1, respectively.

FIG. 5 is a schematic cross sectional illustration of a fifthimplementation of the invention comprising, on a multiple layeredsubstrate, plural of photonic crystals.

FIG. 6 is a photonic bandgap map for a triangular lattice of air columnsdrilled in a dielectric medium.

FIG. 7 is a photonic bandgap map for a honeycomb lattice of dielectriccolumns.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[First Implementation of the Invention]

FIG. 1 is a schematic top view of an exemplary implementation of thetwo-dimensional photonic crystal of the invention. The structureincludes a plurality of elongated first elements 1 formed of a firstdielectric material. It is noted that the term “element or elements” asused herein is intended to encompass, without limitation, bores orspaces which may be filled with fluids or solids such as air and/orother gas, liquid or solid material. The elements 1 extend in parallelto one another. A longitudinal axis, not shown, extends through thecenter of each element 1 in the vertical or z-direction. The elements 1are arranged periodically in two dimensions (x, y) in a plane generallyorthogonal to the longitudinal axes extending through the elements 1.

The elements 1 are generally triangularly shaped, each having agenerally triangular cross sectional profile throughout its longitudinalaxis, and extending in a two-dimensional periodic arrangement relativeto the x-y plane or any plane parallel thereto. The elements 1 areperiodically arranged to provide a honeycomb lattice. The elements 1 canbe simply regions of air or can include any other substantiallydielectric solid, fluid (liquid or gas) or gel material. Althoughgenerally triangular elements are described in connection with FIG. 1,triangular or cylindrical elements or any shaped elongated elements maybe employed without departing from the scope of the invention.

A second dielectric material 2 surrounds each of the plurality ofelongated elements 1 and extends between the elements 1. The seconddielectric material 2 defines between the elongated elements 1 aplurality of spaces or bores filled with a third dielectric material 3.It should be noted that different shadings is used on FIG. 1 todistinguish between the first and second materials and that the thirddielectric material is not shaded.

The permittivity ε1 of the first dielectric material 1 is greater thanthe permittivity ε2 of the second dielectric material 2 and thepermittivity ε3 of the third dielectric material 3. The permittivity ε2of the second dielectric material 2 in greater than the permittivity ε3of the third dielectric material 3. This relation can be expressed as a1>ε2>ε3,

FIG. 1 schematically illustrates a two-dimensional periodic arrangementof bores that are filled with the third dielectric material 3. In theembodiment shown, each of the bores 3 is circular in cross sectionalconfiguration. The two dimensional periodic arrangement of the bores 3is a triangular lattice with lattice constant a, which represents thedistance between centers of the bores 3. As shown in FIG. 1, each of theelements 1 is located within a triangle defined by the bores 3. Thisarrangement of the elements 1 produces a two-dimensional periodichoneycomb lattice.

In this embodiment, each of the elements 1 is a rod of solid material.The rods 1 are surrounded or covered by the second solid dielectricmaterial 2 that extends between the rods 1. This arrangement of thesecond solid dielectric material 2 produces a considerable increase instrength in honeycomb lattice structure of the rods 1 as compared to theconventional honeycomb lattice of rods. According to the conventionalhoneycomb lattice, the rods are spaced with all the spacing materialcompletely removed.

As shown In FIG. 1, each of the elements 1 has a generally triangularcross sectional configuration having three sides. The cross sectionalconfiguration of each element 1 is not limited to the illustratedexample of general triangle. The cross sectional configuration of eachelement 1 may take any other desired shape. The cross sectionalconfiguration of each bore 3 is circular in this embodiment. But it maytake any other desired shape.

It will be appreciated by those skill in the art that dielectricstructures tend to have both transverse-electric (TE) guided modes andtransverse-magnetic (TM) guided modes. TE modes are defined in a uniformdielectric slab as the modes for which the electric field is polarizedparallel to the slab. TM modes are defined in a uniform dielectric slabas the modes for which the magnetic field is polarized parallel to theslab. In the case of a non-uniform dielectric slab, the modes are notpurely TE or purely TM, but rather quasi-TE or quasi-TM.

The lattice structure of the elongated elements 1 have dimensions, whichare proportioned such that the structure defines a complete photonicbandgap (PBG) at a range of frequencies such that electric field at suchfrequencies having a polarization parallel to a plans orthogonal to thelongitudinal axes of the elongated elements 1 (TE modes) and magneticfield at such frequencies having a polarization parallel to of the planeare prevented from propagating within the periodic lattice structure.The photonic crystal shown in FIG. 1 has combined performancesuperiority of honeycomb lattice of the elongated elements 1 withstructural superiority of triangular lattice of bores 3. The honeycomblattice structure provides a wider range of frequencies over a completePBG (see the dotted area TM+TE in FIG. 7) than a range of frequenciesover a complete PBG (see the dotted area TM+TE in FIG. 6) provided bythe triangular lattice structure. The triangular lattice structure isrobuster than the honeycomb lattice structure.

Each element 1 of the photonic crystal that was actually made was formedof Si having dielectric constant of 11.9 and had a generally triangularcross sectional profile having three sides each having 0.4 μm in length.As the second dielectric material 2, SiO₂ with a dielectric constant of3.1 was used. A layer of SiO₂ with a thickness 0.1 μm covered theelongated elements 1. The third dielectric material 3 was air having adielectric constant of 1.

The elements 11 of SiO₂ was arranged in the two-dimensional honeycomblattice pattern having a lattice constant a of 1.55 μm to produce acomplete PBG to forbid the propagation of incident of light with awavelength of 1.55 μm. The honeycomb lattice constant is the distancebetween centers of the adjacent two bores 3.

The engagement of SiO₂ with Si is firmer than the engagement of SiO₂with GaAs. Thus, this firm engagement of the second dielectric material2 with the elongated elements 1 makes at least partial contribution toincreased structural strength of the photonic crystal of the invention.

[Second Implementation of the Invention]

FIG. 1 Is a schematic top view of another exemplary implementation ofthe two-dimensional photonic crystal of the invention. The structureincludes a plurality of elongated first elements 11 formed of a firstdielectric material. The elements 11 extend in parallel to one another.A longitudinal axis, not shown, extends through the center of eachelement 11 in the vertical or z-direction, The elements 1 are arrangedperiodically in two dimensions (x, y) in a plane generally orthogonal tothe longitudinal axes extending through the elements 11.

The elements 11 are rods or columns, each having a circular crosssectional profile throughout its longitudinal axis. The elements 11 areperiodically arranged to provide a honeycomb lattice.

A second dielectric material 12 surrounds each element 11 and extendsbetween the elements 11. The second dielectric material 2 definesbetween the elongated elements 1 a plurality of spaces or bores filledwith a third dielectric material 13. It should be noted that differentshadings is used on FIG. 1 to distinguish between the first and secondmaterials and that the third dielectric material is not shaded.

The permittivity ε1 of the first dielectric material 11 is greater thanthe permittivity ε2 of the second dielectric material 12 and thepermittivity ε3 of the third dielectric material 13. The permittivity ε2of the second dielectric material 12 is greater than the permittivity ε3of the third dielectric material 13.

Each element 11 of the photonic crystal of FIG. 2 that was actually madewas formed of GaAs having a dielectric constant of 13.1 and has acircular cross sectional profile with a diameter of 0.43 μm. As thesecond dielectric material 12, SiO₂ with a dielectric constant of 3.1was used. A layer of SiO₂ with a thickness 0.1 μm covered the elements11. The third dielectric material 13 was air having a dielectricconstant of 1.

The elements 11 of GaAs was arranged in the two-dimensional honeycomblattice pattern having a lattice constant a of 1.55 μm to produce acomplete PBG to forbid the propagation of incident of light with awavelength of 1.55 μm.

[Third Implementation of the Invention]

The photonic crystal shown in FIG. 2 can be fabricated on a portion of ahomogeneous or uniform dielectric substrate by one of several methods.One exemplary method involves the use of etching technique to formdielectric columns in honeycomb periodic pattern and the use ofdeposition to form dielectric film around the columns.

FIGS. 3A-1 to 3C-1 are schematic cross-sectional illustrations showingfabrication steps. FIGS. 3A-2 to 3C-2 are schematic top views showingthe fabrication steps of FIGS. 3A-1 to 3C-1, respectively.

Referring to FIGS. 3A-1 and 3A-2, a dielectric substrate 21 is coveredon one face with an etching mask 22. The etching mask 22 contains atwo-dimensional array of geometric figures of the size, spacing andperiodicity required for the desired complete PBG. If circular rods orcolumns of high dielectric material are to be formed in the substrate,the geometric figures are circles that are opaque to an etchant used toselectively eradicate the high dielectric substrate material, and theremainder of the mask is transparent to the etchant. Photolithography orelectron beam lithography may be employed to pattern the two-dimensionalarray of geometric figures.

If the geometric figures of a patterned resist on the substrate arepositively defined, metal or dielectric is deposited, by vapordeposition, on the substrate to fill the apertures of the geometricfigures and the resist is removed. The resulting two-dimensional arrayof deposited metal or dielectric figures defines the etching mask 22.

If the geometric figures of a patterned resist are negatively defined,it can be directly used as the etching mask 22. Prior to patterning suchresist, one or more thin layers, each being formed of metal ordielectric, may be formed on the face of the substrate. In this case,the resist is formed on the thin layer on the substrate and used as amask for the subsequent dry etching to transfer the pattern to the thinlayer on the substrate. The transferred pattern within the thin layer ofthe substrate also defines the etching mask 22 in cooperation with theresist. If desired, the resist may be removed. Using the transferredpattern from the resist as the mask for the subsequent etching is widelyemployed technique to widen an etch selectivity between substrate andmask.

The pattern of the etching mask 22 is transferred to the underlyingsubstrate 21 by using a dry etcher, and vertical channels of the desiredshape are created in the substrate 21 as shown in FIGS. 3B-1 and 3B-2.The resulting array of elements defines the two-dimensional periodicityof the honeycomb lattice structure. If the etching mask 22 containsmetal, it must be removed. If the etching mask 22 contains dielectricmaterial only, the etching mask 22 may not be removed.

After etching, the substrata 21 with the resulting array is cleaned.Then, a dielectric layer 24 of a dielectric material with a lesspermittivity than the substrate 21 is formed on the substrate 21. Thedielectric layer 24 has a thickness such that the dielectric layer 24extends between the adjacent dielectric rods or columns 23, Thisarrangement makes contribution to increased strength of the photoniccrystal of the invention.

The substrate 21 was a homogeneous substrate of GaAs with a permittivityof 13.1. This substrate 21 was non-doped to suppress absorption of lightto a sufficiently low level. The substrate 21 was coated with a PMMAresist by a spin coater. The thickness of the PMMA resist was 0.2 μm.Then, the resist on the substrate 21 was baked at temperature 80° C. for15 minutes. An electron beam lithography system was used to print on thebaked resist a two-dimensional array of geometric figures of the size,spacing and periodicity required for the desired honeycomb lattice witha lattice constant of 1.55 μm. The geometric figures of the resist werecircular apertures. An electron beam evaporation system was used todeposit Ni on the resist to a depth 50 μm. Then, the substrate 21 inimmersed into organic solvent for removing Ni from the surface or theresist, forming an array of geometric figures of Ni.

Subsequently, using the array of Ni geometric figures as a mask, thesubstrate was etched within an electron cyclotron resonance (ECR) plasmaetching system. Chlorine gas plasma under pressure 13.3 mPa was used asan etchant. The bias voltage applied to the substrate was 70 V. Thetemperature of the substrate was cooled and maintained at roomtemperature. After the etching was completed, the array of Ni geometricfigures was removed from the face of the substrate and the substrate wascleaned by hydrochloride and water. Subsequently, a thermal CVD systemwas used to deposit SiO₂ to a depth 0.1 μm on the substrate.

If desired, SiO₂ on the upper end of each of dielectric rods or columns23 and a portion of SiO₂ within spaces between the rods or columns 23may be removed by exposing the substrate to anisotropic etching within aparallel plate dry etching system. An etchant was CF₄ gas plasma underpressure 0.4 mPa. The bias voltage applied to the substrate was about 30V. If desired, other etching system such as a photo etching system maybe used instead of the above-mentioned parallel plate dry etchingsystem.

The resulting photonic crystal exhibited increased structural strengthbecause SiO₂ interconnect the dielectric rods or columns 23.

[Fourth Implementation of the Invention]

The photonic crystal shown In FIG. 1 can be fabricated on a portion of ahomogeneous or uniform dielectric substrate by one of several methods.One exemplary method involves the use of etching technique to form boresperiodic triangular pattern and the use of oxidation to form dielectriccolumns in periodic honeycomb pattern.

FIGS. 4A-1 to 4C-1 are schematic cross-sectional illustrations showingfabrication steps. FIGS. 4A-2 to 4C-2 are schematic top views showingthe fabrication steps of FIGS. 4A-1 to 4C-1, respectively.

Referring to FIGS. 4A-1 and 4A-2, a dielectric substrate 31 is coveredon one face with an etching mask 32. The etching mask 32 contains atwo-dimensional array of geometric figures of the size, spacing andperiodicity required for a triangular lattice with a lattice constant athat is equal to a lattice constant of a desired honeycomb lattice. Ifcircular holes or bore are to be formed in the substrate, the geometricfigures of the etching mask 32 are circles that are transparent to anetchant used to selectively eradicate the high dielectric substratematerial, and the remainder of the mask is opaque to the etchant.Photolithography may be employed to pattern the two-dimensional array ofsuch geometric figures.

The pattern of the etching mask 32 is transferred to the underlyingsubstrate by using a dry etcher, and vertical channels of the desiredshape, i.e., bores 33, are created in the substrate 31 as shown in FIGS.4B-1 and 4B-2. The resulting array of elements defines thetwo-dimensional periodicity of bores 33 in triangular lattice structure.

After etching, the substrate 31 with the resulting array is cleaned.Then, the substrate 31 is oxidized. Oxidation progresses inwards of thesubstrate from a cylindrical wall defining each bore 33 until portionsof the substrate dielectric material on line segments, eachinterconnecting the centers of the adjacent two bores 33, are completelyoxidized. Oxidation has progressed inwards from the wall defining eachbore 33 forms an oxide layer 34 as shown in FIGS. 4C-1 and 4C-2.Oxidation causes the permittivity of the dielectric material of thesubstrate 31 to drop. Thus, the oxide layer 34 has a permittivity lessthan the dielectric material of the substrate 31. The thickness of eachoxide layer 34 is determined such that the three oxide layers 34extending toward each other from three bores 33 that are in a singletriangular lattice cooperate with each other to leave a generallytriangular column of the substrate dielectric material non-oxidized. Theresulting array of these triangular dielectric columns defines thetwo-dimensional array of dielectric columns 35 in the desired honeycomblattice, as shown in FIG. 1.

The thickness of each oxide layer 34 may be slightly less than theabove-mentioned thickness at which portions of the substrate dielectricmaterial on line segments, each interconnecting the centers of theadjacent two bores 33, are completely oxidized as long as each ofdielectric columns 35 is substantially surrounded by the three oxidelayers 34. In this case, the same structure might be fabricated byforming an oxide layer on a cylindrical wall defining each bore 33. But,this method requires etching bores in triangular lattice with a verythin separating wall between the adjacent two of the bores. Thus, if aphotonic crystal with a very thin separating wall between the adjacenttwo of bores in triangular lattice is to be formed, the method accordingto the fourth implementation of the invention is advantageous becausethe oxidation inwards from the bore defining walls allows etching bores33 leaving sufficiently thick separating walls between them.

The substrate 31 was a homogeneous substrate of Si with a permittivityof 11.9. This substrate 31 was non-doped to suppress absorption of lightto a sufficiently low level. The substrate 31 was coated with a photoresist by a spin coater. The thickness of the photo resist was 1 μm.Then, the photo resist on the substrate 31 was baked at temperature 80°C. for 15 minutes. An i-line stepper was used to print in the bakedphoto resist a two-dimensional array of geometric figures of the size,spacing and periodicity required for the desired triangular lattice witha lattice constant of 1.55 μm. The geometric figures of the photo resistwere circular apertures with a diameter of 1.40 μm.

Subsequently, using the patterned photo resist as a mask, an ECR plasmaetching system was used to etch the substrate. Chlorine gas plasma underpressure 13.3 mPa was used as an etchant. The bias voltage applied tothe substrate was 70 V. The temperature of the substrate was cooled andmaintained at room temperature. After the etching was completed, thephoto resist was removed from the face of the substrate by cleaning withorganic solvent. Subsequently, a thermal oxidation furnace was used tooxide the substrate inwards to a depth 0.1 μm from a cylindrical walldefining each bore 33 to form a layer of SiO₂. The temperature withinthe furnace was 950° C.

The three oxide layers 34 extending toward each other from three bores33 that are in a single triangular lattice cooperate with each other toleave a generally triangular column of the substrate dielectric materialnon-oxidized. The resulting array of these triangular dielectric columnsdefines the two-dimensional array of dielectric columns 35 in thedesired honeycomb lattice, as shown in FIG. 1.

If desired, SiO₂ on the upper end of each of dielectric columns 35 and aportion of SiO₂ within spaces between the columns 35 may be removed byexposing the substrate to anisotropic etching within a parallel platedry etching system. An etchant was CF₄ gas plasma under pressure 0.4mPa. The bias voltage applied to the substrate was about 30 V. If thestructure can withstand stress, hydrofluoric acid may be used to removea portion of SiO₂.

The preceding description on the fourth implementation clearly indicatesthat forming or patterning a resist for the subsequent etching bores intriangular lattice does not require excessive accuracy. In the thirdembodiment, a resist for the subsequent etching elements in honeycomblattice requires high accuracy to form.

If dielectric elements in honeycomb lattice with a lattice constant 1.55μm are to be formed, the distance between centers of the nearest twodielectric elements is 0.89 μm. According to the third implementation ofthe invention, a resist must include geometric figures in honeycomblattice with their centers separated one after another by a distance0.89 μm. In this case, what is needed to form the geometric figures onthe resist in an electron beam lithography system rather than an i-lineor g-line stepper. According to the fourth implementation of theinvention, a resist must include geometric figures in triangular latticewith their centers separated one after another by a distance 1.55 μm. Inthis case, an i-line or g-line stepper can be used in forming thegeometric figures. It is known that although the stepper is inferior tothe electron beam lithography in terms of resolution of image, thestepper is better for mass production than the electron bean lithographywhen comparing them in terms of throughput.

The dielectric substrate 31 may be made of GaAs or appropriate one ofchemical compounds of elements belonging to III-V groups. However, theuse of Si as the material of dielectric substrate 31 is advantageousbecause the fully developed and stable thermal oxidation technique of Sican be used.

According to the fourth implementation of the invention, the thicknessof oxide layer determines dimensions of each dielectric elongatedelement along the plane orthogonal (x-y plane) to the longitudinal axesof the dielectric elements. According to the thermal oxidationtechnique, it is quite easy to control the thickness of oxide layer.Thus, what is needed is to alter the thickness of oxide layer only totune a photonic crystal within a range of frequencies over PBG.

[Fifth Implementation of the Invention]

FIG. 5 is a schematic cross section illustrating the fifthimplementation of the invention. According to the fifth implementation,a photonic crystal is formed in a multiple layer substrate. In FIG. 5,the reference numeral 41 designates a substrate. The reference numeral42 designates a dielectric layer formed of a dielectric material with alow permittivity. The reference numeral 43 designates a two-dimensionalphotonic crystal.

An example of the illustrated structure can be provided by forming aphotonic crystal of the first or second implementation in an Si layer ofa SOI (Si on Insulator: Si/SiO₂/Si) substrate if the SOI substrate is tobe used as the multiple layer substrate.

In this case, the two-dimensional photonic crystal 43 is interposedbetween the dielectric layer 42 with low permittivity and air with lowpermittivity. This structure is analogous to a slab waveguide andrestrains the propagation of light in a vertical direction parallel tothe longitudinal axes of dielectric elements in honeycomb lattice. Thus,the proipagation of light into the low dielectric layer 42 and/or air issuppressed.

While the present invention has been particularly described, inconjunction with a preferred embodiment, it is evident that manyalternatives, modifications and variations will be apparent to thoseskilled in the art in light of the foregoing description. It istherefore contemplated that the appended claims will embrace any suchalternatives, modifications and variations as falling within the truescope and spirit of the present invention.

What is claimed is:
 1. A photonic crystal comprising: a plurality ofelongated elements formed of a first dielectric material and arranged ina two-dimensional periodic honeycomb lattice; and a second dielectricmaterial surrounding said plurality of elongated elements and extendingbetween said plurality of first elements, said second dielectricmaterial defining between said elongated elements a plurality of spacesfilled with a third dielectric material, said first dielectric materialhaving permittivity that is greater than permittivity of said seconddielectric material and permittivity of said third dielectric material.2. The photonic crystal as claimed in claim 1, wherein said firstdielectric material is selected from a first group consisting of Si andGaAs, said second dielectric material is selected from a groupconsisting of SiO₂, SiN_(x) and SiO_(x)N_(y).
 3. The photonic crystal asclaimed in claim 1, wherein said elongated elements, second and thirddielectric materials are formed on a substrate.